Biomedical

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 60, NO. 5, MAY 2013 1345

Fetal ECG Extraction by Extended State KalmanFiltering Based on Single-Channel Recordings

Mohammad Niknazar∗, Bertrand Rivet, and Christian Jutten, Fellow, IEEE

Abstract—In this paper, we present an extended nonlinearBayesian filtering framework for extracting electrocardiograms(ECGs) from a single channel as encountered in the fetal ECGextraction from abdominal sensor. The recorded signals are mod-eled as the summation of several ECGs. Each of them is describedby a nonlinear dynamic model, previously presented for the gen-eration of a highly realistic synthetic ECG. Consequently, eachECG has a corresponding term in this model and can thus beefficiently discriminated even if the waves overlap in time. Theparameter sensitivity analysis for different values of noise level,amplitude, and heart rate ratios between fetal and maternal ECGsshows its effectiveness for a large set of values of these parame-ters. This framework is also validated on the extractions of fetalECG from actual abdominal recordings, as well as of actual twinmagnetocardiograms.

Index Terms—Extended Kalman filtering (EKF), fetal electro-cardiogram (fECG) extraction, model-based filtering, nonlinearBayesian filtering, twin magnetocardiogram (MCG) extraction.

I. INTRODUCTION

S INCE the first demonstration of the fetal electrocardiogram(fECG) carried out in 1906 by Cremer [1], various methods

for fECG monitoring have been proposed to obtain informationabout the heart status. The fECG can be measured by placingelectrodes on the mother’s abdomen. However, it has very lowpower and is mixed with several sources of noise and inter-ference. Nevertheless, the main contamination is the maternalelectrocardiogram (mECG) [2]. As a result, the basic problemis to extract the fECG signal from the mixture of mECG andfECG signals, where the interfering mECG is a much strongersignal. According to the review [3], existing fECG extractionapproaches in the literature can be categorized by their method-ologies, which include linear or nonlinear decomposition andadaptive filtering.

Linear or nonlinear decomposition methods are commonapproaches, in which single- or multichannel recordings are

Manuscript received February 20, 2012; revised May 7, 2012, October 1,2012, and November 27, 2012; accepted November 29, 2012. Date of publicationDecember 20, 2012; date of current version April 15, 2013. Asterisk indicatescorresponding author.

∗M. Niknazar is with the GIPSA-lab (UMR CNRS 5216), University ofGrenoble, Grenoble 38402, France (e-mail: [email protected]).

B. Rivet is with the GIPSA-lab (UMR CNRS 5216), University of Grenoble,Grenoble 38402, France (e-mail: [email protected]).

C. Jutten is with the GIPSA-lab (UMR CNRS 5216), University of Grenoble,Grenoble 38402, France, and also with the Institut Universitaire de France,75005 Paris, France (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TBME.2012.2234456

decomposed into different components using suitable basisfunctions. Linear decomposition methods use either fixed ba-sis functions (e.g., wavelets [4]), or data-driven basis functions(e.g., singular vectors [5]). This limits performance of decompo-sition in nonlinear or degenerate mixtures of signal and noise [3].Blind or semiblind source separation, which are categorized aslinear decomposition approach, have also been used for fECGextraction [6], [7]. These methods are based on the assumptionof independent components (or more generally independent sub-spaces [8] or partitions [9]) for the maternal and fetal signals,or of the existence of some temporal structure for the desiredsignals [10]–[12]. In [13] and [14], wavelet decomposition wasalso combined with blind source separation for extracting anddenoising fECG signals. In another recent work, a new techniquewas proposed to fasten the traditional independent componentanalysis (ICA) method [15]. In blind source separation meth-ods, it is usually assumed that signals and noises are mixed ina stationary and linear manner. However, fECG and other inter-ferences and noises are not always stationary mixed and linearlyseparable [16].

Nonlinear transforms have been also used for mECG can-celation and fECG extraction. In these methods, constructedphase space of noisy signal and of its delayed versions issmoothed using conventional or principal component analysis(PCA) smoothers [17]. The samples are then transferred backto the time-domain representation. Although these methods areinteresting since they are applicable to as few as one singlematernal abdominal channel, the selection of the required timelags for constructing phase space representation is empirical andthe important interbeat variations of the cardiac signals can bewiped-out during the state-space smoothing. Moreover, they de-mand higher computational complexity in comparison to linearmethods, and the correct embedding dimension can change asthe noise statistics change [3].

Adaptive filtering is another common approach for mECGcancelation and fECG extraction [18]. The conventional adap-tive filtering is based on training an adaptive filter for eitherremoving the mECG using one or several maternal referencechannels [18], [19], or directly training the filter for extract-ing the fetal QRS waves [20], [21]. However, existing adaptivefiltering methods for mECG artifact removal either require areference mECG channel that is morphologically similar to thecontaminating waveform or require several linearly independentchannels to roughly reconstruct any morphologic shape from thereferences [18]. Both of these approaches are practically incon-venient and with limiting performance, because the morphologyof the mECG contaminants highly depends on the electrode lo-cations and it is not always possible to reconstruct the complete

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1346 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 60, NO. 5, MAY 2013

mECG morphology from a linear combination of the referenceelectrodes [3]. Practically, it has been shown that for fECG ex-traction, blind source separation methods outperform adaptivefilters [22]. An important advantage of spatial filtering over con-ventional adaptive filters is their ability to separate mECG andfECG with temporal overlap but it often requires more than twosensors.

The Kalman filtering (KF) framework, which can be consid-ered as a member of the general class of adaptive filters, is apromising approach for both mECG cancelation and fECG en-hancement. In [16] and [23], a set of state-space equations wasused to model the temporal dynamics of ECG signals, for de-signing a Bayesian filter for ECG denoising. This Bayesian filterframework was used in [16, p. 50] to extract fECG from single-channel mixture of mECG and fECG. However, as mentionedin [16], the filter fails to discriminate between the maternal andfetal components when the mECG and fECG waves fully over-lap in time. The reason is that when mECG is being estimated,fECG and other components are supposed to be Gaussian noises.However, this assumption is not true, especially when mECGand fECG waves fully overlap in time it is difficult for the filterto follow desired ECG.

Clinical monitoring of fetal cardiac activity is usually basedon a small number of electrodes located on mother’s abdomen,and on a sound sensitive sensor. In such a context, in this study,we wonder what performance can be obtained with only oneelectrode, by using a refined model of the signal recorded on theunique electrode: the model will explicitly take into account thatthe signal is the superposition of a few ECG signals. The rest ofthis paper is organized as follows. In Section II, equations andtheory supporting our proposed method including the Bayesianfiltering theory and dynamic ECG model are described. In Sec-tion III, results of the proposed method applied on differentdata and discussion about the results are presented. Finally, ourconclusion is stated in Section IV.

II. METHODOLOGY

A. Extended Kalman Filter Framework for ECG Extraction

The goal of KF is to estimate the state of a discrete-timecontrolled process. Consider a state vector xk+1 governed bya nonlinear stochastic difference equation with measurementvector yk+1 at time instant k + 1:

{xk+1 = f(xk ,wk , k + 1)yk+1 = h(xk+1 ,vk+1 , k + 1)

(1)

where the random variables wk and vk represent the pro-cess and measurement noises, with associated covariance ma-trices Qk = E

{wkwT

k

}and Rk = E

{vkvT

k

}. The extended

Kalman filter (EKF) is an extension of the standard KF to non-linear systems f(·) and h(·), which linearizes about the cur-rent mean and covariance [24]. In order to improve the estima-tions, EKF can be followed by a backward recursive smoothingstage leading to the extended Kalman smoother (EKS). How-ever, since EKS is a noncausal method, it cannot be appliedonline but it is useful if a small lag in the processing is allowed.

Fig. 1. Illustration of the phase assignment approach on one ECG.

In this study, a synthetic dynamic ECG model [25] is usedto extract fECG from mixture of an mECG, one (or more)fECG(s), and other signals considered as noises. In polarcoordinates [23], one ECG signal can be expressed as thesum of five Gaussian functions defined by their peak ampli-tude, width, and center, denoted αi , bi , and ψi , respectively:z(θ) =

∑i∈W αi exp(−(θ − ψi)2/(2b2

i )). Each Gaussian func-tion thus models one of the five waves W = {P,Q,R, S, T} ofa heart beat. The state vector in (1) is defined by the phase θand the amplitude z of the ECG: xk = [θk , zk ]T . Assuming asmall sampling period δ, the state noise ηk , and defining wk as[0, ηk ]T , the state process f(·) is

θk+1 = (θk + ωδ) mod(2π) (2)

zk+1 = −∑i∈W

αiΔθi,kωδ

b2i

exp

(−

Δθ2i,k

2b2i

)+ zk + ηk (3)

where ω is the phase increment and Δθi,k = (θk − ψi)mod(2π). From the ECG, one can define the observed phaseφk by a linear time wrapping of the R–R time intervals into[0, 2π) (see Fig. 1). The measurement process h(·) is finally de-fined as yk+1 = xk+1 + vk+1 , where yk+1 = [φk+1 , sk+1]T .

The ECGs composing the observed mixture can be estimatedby recursively applying the described EKF: at each step, oneECG is extracted according to a deflation procedure. In case of amixture of mECG and one fECG, the first step extracts, from theraw recording, the dominant ECG (often the mECG) consideringthe concurrent ECG (respectively, fECG) and other noises as aunique Gaussian noise. After subtracting the dominant ECGfrom the original signal, the second step is the extraction offECG from the residual signal. This procedure is referred to assequential EKF or EKS (seq-EKF or seq-EKS). In this recursiveextraction, during the first step, the concurrent ECG (i.e., fECG)and additional noise are modeled by Gaussian noises vk and wk ,which is not a very relevant assumption. In fact, although thisassumption may be acceptable when there are not strong artifactsinterfering with the ECG, it is no longer accurate when otherECG artifacts are considerable (i.e., at the first step) since thenoise is no longer normally distributed. In addition, concurrentECGs can be confused with dominant ECG when their waves(especially QRS complexes) fully overlap in time. Meanwhile,resultant inaccuracies, which are generated by the previous stepsof the ECG extraction, will propagate to the next steps while theresiduals are computed.

NIKNAZAR et al.: FETAL ECG EXTRACTION BY EXTENDED STATE KALMAN FILTERING BASED ON SINGLE-CHANNEL RECORDINGS 1347

B. Extension to Multiple ECGs: Extended State EKF

In this paper, the dynamic equations (2) and (3) are ex-tended for simultaneously modeling N ECGs mixed in asingle observation. The related extended state vector xk =[θ(1)

k , z(1)k , . . . , θ

(N )k , z

(N )k ]T is thus defined by⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

θ(1)k+1 = (θ(1)

k + ω(1)δ) mod(2π)

z(1)k+1 = −

∑i∈W1

α(1)i ω(1)δ

b(1)2

i

Δθ(1)i,k exp

(−

Δθ(1)2

i,k

2b(1)2

i

)

+z(1)k + η

(1)k

...

θ(N )k+1 = (θ(N )

k + ω(N )δ) mod(2π)

z(N )k+1 = −

∑i∈WN

α(N )i ω(N )δ

b(N )2

i

Δθ(N )i,k exp

(−

Δθ(N )2

i,k

2b(N )2

i

)

+ z(N )k + η

(N )k

where each [θ(i)k , z

(i)k ]T is related to one of the ECGs. Finally, the

measurement process leads to express the measurement vectoryk+1 = [φ(1)

k+1 , . . . , φ(N )k+1 , sk+1]T as⎧⎪⎪⎨

⎪⎪⎩φ

(n)k+1 = θ

(n)k+1 + v

(n)k+1 , ∀n ∈ {1, . . . , N}

sk+1 =N∑

n=1

z(n)k+1 + v

(N +1)k+1 .

(4)

This extended state Kalman filtering procedure is referred to asparallel EKF or EKS (par-EKF, or par-EKS, respectively). Asshown in Section III, this par-EKF or par-EKS is more accurateto extract fECG from abdominal sensors than the seq-EKF orseq-EKF. Indeed, in the proposed method, all ECGs are jointlymodeled by dynamic states so that only the state and mea-surement noise vectors are assumed to be normally distributed.Moreover, the extended state par-EKF fully models overlappingwaves of several ECGs. Finally, the state and observation noises,ηn

k and vnk , respectively, allow the filter to fit some variabilities

of the ECG shapes. Although the model does not fit too largevariations (for example, due to arrythmia), an inspection of theresidue will reveal these abnormal beats.

C. Model Parameters Estimation

The proposed par-EKF and par-EKS lie on several state pa-rameters {α(n)

i , b(n)i , ψ

(n)i }i∈Wn

, ∀n ∈ {1, . . . , N}. The proce-dure described below is an extension of the single ECG param-eter estimation [23].

The parameters estimation procedure first needs the R-peakdetection for all ECGs to perform the time wrapping of the R–Rintervals into [0, 2π) to define φ

(n)k . The R-peaks are found from

a peak search in windows of length T , where T corresponds tothe R-peak period calculated from approximate ECG beat-rate.R-peaks with periods smaller than T

2 or larger than T are notdetected. Although maternal R-peaks are easily detectable fromthe mixture, fetal R-peak detection is more complex due to itslower amplitude than mECG. Therefore, a rough estimation of

fECG is obtained by using the seq-EKF algorithm, which nowallows us to detect easily the fetal R-peaks.1 Then, for each ECG,each beat (defined by the signals between two consecutive R-peaks) is time wrapped into [0, 2π). The average of the ECGwaveform is obtained by the mean of all time-wrapped beats,for all phases between 0 and 2π. Finally, by using a nonlinearleast-squares approach [26], the best estimate of the parametersin the minimum mean square error (MMSE) sense is found.

III. RESULTS AND DISCUSSIONS

Both synthetic and actual data have been used to study perfor-mance of the proposed method. In Subsection III-A, quantitativeresults coming from simulations and influence of the main pa-rameters of mixed ECGs on performance of the method has beenstudied. They will present the conditions in which the proposedmethod is efficient. In Subsection III-B, the effectiveness of themethod on actual data has been examined.

A. Experimental Performance Analysis on Synthetic Data

Since there is neither ground truth nor golden standard onsingle-channel recording, it is important to provide quantitativeperformance with simulations to validate the behavior of theproposed method. In order to do so, realistic synthetic mixturesof mECG and fECG with white Gaussian noise have been gener-ated for different situations, and the proposed method has beenapplied on them to extract mECG and fECG.

Synthetic mECG and fECG used in this study are based on a3-D canonical model of the single dipole vector of the heart, pro-posed in [27] and inspired by the single-channel ECG dynamicmodel presented in [25]. Sampling frequency is set to 500 Hzand signals include 20 000 samples. The main parameters thatcan affect the mixtures are input noise power, ratio betweenamplitudes of fECG and mECG, and ratio between fetal andmaternal heart rates. In order to investigate the performance ofthe proposed method, 100 trials were carried out under eachvalue of these parameters. In the output, estimated mECG andfECG signals, sm and sf , are assumed to be the sum of mECG,fECG, and noise, such that

sm = α1sm + α2sf + α3n

sf = β1sm + β2sf + β3n (5)

where coefficients α1 , α2 , α3 , β1 , β2 , and β3 have to be es-timated and sm , sf , and n denote mECG, fECG, and noise,respectively. In order to estimate the coefficients, sm , sf , and nare assumed to be orthogonal, i.e., decorrelated. The orthogo-nality principle states that an estimator s achieves MMSE if andonly if E

{(s − s)T s

}= 0. Satisfaction of this criterion leads to

α1 =E(sT

m sm )E(sT

m sm ), α2 =

E(sTm sf )

E(sTm sf )

, α3 =E(sT

m n)E(sT

m n)

β1 =E(sT

f sm )E(sT

f sm ), β2 =

E(sTf sf )

E(sTf sf )

, β3 =E(sT

f n)E(sT

f n). (6)

1In practice, one could also use a sound sensor to have a reliable R-peakdetector. In this case, even if there exists a delay, it does not impact the method,since it can be synchronized.


Fig. 2. Mean SNR improvement results of the EKF and EKS against inputnoise power (bold lines). Upper and lower borders (thin lines) present maximumand minimum, respectively.

In a successful estimation, contribution of desired ECG inoutput should be much more than contribution of undesired ECGand noise. In other words, in extraction of fECG, the power ofβ2sf should be much larger than the power of β1sm + β3n,which means the contribution of mECG and noise is very lowin the fECG estimate. In the same manner, the power of α1sm

should be much larger than the power of α2sf + α3n in mECGextraction. In order to quantize contribution of the desired ECGin the output, output signal-to-noise ratio (SNR) for maternaland fetal ECGs are defined as

SNRm o u t =α2

1Psm

α22Psf

+ α23Pn

SNRfo u t =β2

2 Psf

β21 Psm

+ β23 Pn

(7)

where Psm, Psf

, and Pn denote power of mECG, fECG, andnoise, respectively. Output SNR is now compared to input SNRto investigate performance of desired ECG extraction. InputSNRs are defined as

SNRm in =Psm

Psf+ Pn

and SNRf i n =Psf

Psm+ Pn

. (8)

Input signal-to-interference ratio (SIR) and output SIR arealso defined as

SIRm in =Psm

Psf

, SIRf i n =Psf

Psm

SIRm o u t =α2

1Psm

α22Psf

, SIRfo u t =β2

2 Psf

β21 Psm

. (9)

1) SNR Analysis: Fig. 2 shows SNR improvement results ofEKF and EKS over a wide range of input noise power. The SNRimprovement in decibels is defined as the output SNR of thefilter minus the input SNR. In all trials, power of mECG signalsis normalized to 1 (0 dB) and the ratio of amplitudes of fECGand mECG is 0.3. Maternal and fetal heart rates are set to 1.1

Fig. 3. Mean SIR improvement results of the EKF and EKS against amplituderatio (bold lines). Upper and lower borders (thin lines) present maximum andminimum, respectively.

and 2 Hz, respectively. Moreover, in order to have more realisticsignals, mECG and fECG are allowed to have slight randomfluctuations (5%) in amplitude and duration at each beat. More-over, initial phases of ECGs are random. As can be seen inFig. 2, both EKF and EKS successfully improved the SNR forall ranges of the input SNRs. When the mixture is rather noisefree (noise power −30 dB), the minimum SNR improvement offECG is 40 dB, which means efficient cancelation of mECG.Nevertheless, even for very noisy mixtures (noise power 20 dB),the SNR improvement of fECG remains over 20 dB. Accordingto this figure, EKF is more effective when a rather clean sig-nal is available. On the contrary, as power of noise increases,EKS significantly outperforms EKF. As it has been explainedin the previous section, the EKS algorithm consists of a for-ward EKF stage followed by a backward recursive smoothingstage. Therefore, if a rather clean signal is available, the recur-sive smoothing stage will deteriorate EKF output, because theoutput is smooth enough and recursive smoothing leads to over-filtering. Conversely, if the signal is very noisy, EKF output isnot denoised enough yet. Therefore, recursive smoothing stagecan be successfully used to cancel more noise from the signal.

2) Amplitude Ratio Analysis: The basic problem of fECGmonitoring is to extract the fECG signal from the mixture ofmECG and fECG signals, where the interfering mECG is astronger signal. Therefore, it is necessary to evaluate the perfor-mance of the method for different ratios of fECG and mECGamplitudes. For this purpose, SIR improvement of output signalshave been calculated in the range of 0.1–1 of amplitude ratioof fECG and mECG. Fig. 3 shows SIR improvement resultsof the EKF and EKS for different values of amplitude ratios.Power of mECG signals are normalized to 1 (0 dB) with 5%random fluctuation, input SNR with respect to (w.r.t.) mECG is10 dB, and average maternal and fetal heart rates are 1.1 and2 Hz, respectively. As is seen in Fig. 3, although the fetal SIRimprovements of both EKF and EKS remain over 30 dB for allranges of the amplitude ratios, results of EKS are slightly better.


Fig. 4. Mean SIR improvement results of the EKF and EKS against heart rateratio (bold lines). Upper and lower borders (thin lines) present maximum andminimum, respectively.

3) Heart Rate Ratio Analysis: Since fetal heart rate may varyin a wide range [28], the performance of the method was studiedon a wide range of 0.3–3.6 Hz of fetal heart rate. Fig. 4 showsSIR improvement results of EKF and EKS. Power of mECGsignals are normalized to 1 (0 dB) with 5% random fluctuationand the ratio of amplitudes of fECG and mECG is 0.3. InputSNR w.r.t. mECG is 10 dB, and maternal heart rate is set to1.1 Hz. In this section, heart rate fluctuations are slighter (1%)to study harmonic issues more accurately. As expected, SIRimprovement diagram has three deep local minima at ratios 1,2, and 3. The reason is that when main frequencies of mECGand fECG are proportional, the signals overlap more closelyin the frequency domain. Therefore, discrimination of mECGand fECG is more difficult for these ratios. Nevertheless, thesesituations are unlikely happening because the heart rate ratio isusually more than 1 and less than 2. Even in these cases, fetalSIR improvement remains over 20 dB. Here again, EKS slightlyoutperforms EKF.

B. Fetal ECG Extraction on Actual Data

In Subsection III-A, efficiency of the proposed method infECG extraction for a wide range of possible configurations hasbeen examined using synthetic data. In this section, the results ofapplication of the proposed method on actual data are presented.

1) DaISy Database: The DaISy fetal ECG database [29]consists of a single dataset of cutaneous potential recording ofa pregnant woman. A total of eight channels (five abdominaland three thoracic) are available, sampled at 250 Hz and lasting10 s.

Fig. 5 presents the results of par-EKS and seq-EKS using thefirst channel of the dataset. Moreover, the periodic componentanalysis (πCA) [8] using the eight channels, which is a multi-channel method, is also included as the golden standard. Resultsof πCA method are then postprocessed via EKS on the best ECGestimate [23]. As already mentioned, unlike seq-EKS, par-EKSdoes not fail when mECG and fECG fully overlap in time. This

Fig. 5. Comparison of fECG extraction by par-EKS, seq-EKS and πCA onthe first channel of DaISy data.

is particularly noticed between t = 6 s and t = 7 s in Fig. 5, inwhich some parts of fECG signal have been deteriorated duringmECG extraction by the seq-EKS method. On the contrary, theproposed par-EKS jointly models the fECG and mECG, result-ing in a better estimate of fECG than seq-EKS. Since par-EKSestimates a single component while πCA can estimate severalcomponents (typically one or two), the cosine between sub-spaces is used and is equal to 0.92 in this experiment. With avalue close to 1, these estimates are quite similar. Finally, Fig. 6shows the results of fECG extraction using par-EKS applied onthe other abdominal channels of the DaISy dataset. It experi-mentally proves that par-EKS is able to extract fECG even inill-conditioned mixtures, such as channels 4 or 5.

2) Noninvasive fECG Database: This database consists ofa series of 55 multichannel abdominal fECG recordings, takenfrom a single subject between 21 and 40 weeks of pregnancy.The recordings include two thoracic signals and three or fourabdominal signals. The signals were recorded at 1 kHz, 16-bitresolution with a bandpass filter (0.01–100 Hz) and a main notchfilter (50 Hz) [30]. Fig. 7 shows results of seq-EKS and par-EKSusing channel 3, and πCA using all channels of the first 20s ofnamely the ecgca771 dataset. To show the effectiveness of theproposed method in extraction of the fECG at different periodsof pregnancy, and from different channel locations, the first20s of the mixtures and fetal par-EKS outputs of the datasetsecgca274 channel 5, ecgca748 channel 4, and ecgca997 channel3 are plotted in Fig. 8.

3) Twin Magnetocardiograms Extraction: The proposedmethod has been principally designed for ECG signals. Nev-ertheless, due to the morphological similarity of the ECG andthe magnetocardiogram (MCG), it is also directly applicableto MCG recordings. In this section, twin fetal cardiac mag-


Fig. 6. Results of fECG extraction using par-EKS applied on channels 2–5of the DaISy dataset (up to down). Note differences of scales, according to thechannels and the fetal estimates.

Fig. 7. Comparison of fECG extraction by par-EKS, seq-EKS, and πCA onecgca771 of the PhysioNet database.

netic signals recorded by a SQUID Biomagnetometer systemare extracted. The dataset has been recorded in the BiomagneticCenter of the Department of Neurology (Friedrich Schiller Uni-versity, Jena, Germany) and it consists of 208 channels sampledat 1025 Hz over 30 min.

Fig. 8. ECG mixtures of the datasets ecgca274 channel 5, ecgca748 channel4, and ecgca997 channel 3, and their fetal par-EKS outputs.

Fig. 9. Results of the seq-EKS, par-EKS, and πCA on twin MCG data.

Fig. 9 presents the results of the proposed par-EKS to ex-tract the two fetal MCG signals from a single sensor. A typicalchannel (indexed 92) of namely the q00002252 dataset has beenselected. Even though the multichannel πCA method providesbetter results in this case than single-channel methods (par-EKS


Fig. 10. MCG mixtures of the channels 126, 152, and 160, and their fetalpar-EKS outputs.

or seq-EKS), the proposed par-EKS succeeds to extract the twofetal MCG (fMCG), while seq-EKS fails to discriminate cor-rectly the two fMCGs when they overlap (see highlighted signalparts in Fig. 9). In order to show the good behavior of par-EKSin several configurations, par-EKS is applied on other sensors(see Fig. 10). One can note that the proposed par-EKS succeedsto extract the two fetal MCGs.

Finally, it is worth noting that the crucial part of the proposedpar-EKS is the R-peak detection. Although this detection is quitedirect when a single fetus is present (see Subsection II-C), somewords should be added on twin data. Indeed, on such data, thedetection of the mother’s R-peaks is still direct since it is thedominant signal. On the contrary, the discrimination between thetwo fetal R-peaks is much more difficult. Even though in thisstudy, the oracle is obtained using several sensors and applyingan ICA algorithm (here, we used Fast-ICA), it can be replacedin practice by a sound sensor located on the mother’s abdomen.

IV. CONCLUSION

In this paper, a synthetic dynamic ECG model within a KFframework has been extended to jointly model several ECGs toextract desired ECGs from a unique mixture (i.e., one channelrecording) of maternal and fetal ECGs and noise. Although theproposed method only uses a single channel to separate dif-ferent ECGs, since each ECG has a corresponding term in themodel, the proposed model can efficiently discriminate ECGseven if desired and undesired ECG waves overlap in time. Asproved on synthetic data and illustrated on actual data (singleand multiple fetal pregnancy), the main merit of the proposedalgorithm relies on its performance in a large class of situations.

Performance of the proposed method on extraction of fECGfrom one mixture of mECG and fECG was examined accordingto noise level, amplitude ratio, and heart rate ratio parameters:results show that the proposed method can be successfully em-ployed in many scenarios. According to the obtained results,as long as R-peaks are correctly detected, the proposed modelachieves good results. Although a reliable R-peak detection isa straight forward procedure in a single fetal pregnancy (whichmost likely happens) even with a single sensor, it is much moredifficult in multiple fetal pregnancy (twin or more). Nonethe-less, in these situations, the R-peak detection can be providedby other modalities such as echocardiography.

Finally, the proposed method compares favorably with ef-ficient multisensor methods such as πCA (which also requiresreliable R-peak detection), while it requires only one sensor. Thelatter criterion is of high interest, since using a single channeldoes not only mean less electronic components (such as analogto digital converters or amplifiers) and thus a cheaper device,but also a more convenient and portable device for a long-termmonitoring system or at home since only a single electrode hasto be placed on the mother’s abdomen.

Perspectives include extension of the proposed method toapply on multichannel (but with a small number of channels,e.g., up to 3 or 4) mixtures of mECG and fECG. Moreover,synchronous echocardiography data can also be used in futureworks, especially for a reliable R-peak detection.

ACKNOWLEDGMENT

The authors would like to thank Dr. R. Sameni for his supportand assistance in this study, and Dr. D. Hoyer for providing thetwin MCG dataset.

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Mohammad Niknazar was born in Tehran, Iran, in1985. He received his B.Sc. degree in electrical elec-tronic engineering from the University of Semnan,Semnan, Iran, in 2007, and the M.Sc. degree in elec-trical biomedical engineering from the Sharif Univer-sity of Technology, Tehran, Iran, in 2010. As a mem-ber of GIPSA-lab, he is currently working toward thePh.D. degree in signal, image and speech processingand telecommunications at Joseph Fourier Univer-sity, Grenoble, France.

His research interests include signal and imageprocessing, nonlinear (chaos) analysis, blind source separation, and patternrecognition. Current areas of application include fetal ECG extraction and ECGprocessing. Previous areas of application include epileptic seizure detection andprediction.

Bertrand Rivet was graduated from the EcoleNormale Superieure de Cachan, France. He receivedthe Agregation de Physique Appliquee in 2002, theMaster’s degree from the University of Paris-XI,France, in 2003, and the Ph.D. degree from GrenobleInstitute of Technology (GIT), Grenoble, France, in2006.

He is currently an Associate Professor in signalprocessing with PHELMA and a member of GIPSA-lab, GIT. His research interests include biomedicalsignal processing, audiovisual speech processing, and

blind source separation.

Christian Jutten (F’08) received the Ph.D. degreeand the Docteur es Sciences degree from the Insti-tut National Polytechnique of Grenoble, Grenoble,France, in 1981 and 1987, respectively.

From 1982 to 1989, he was an Associate Professorin the Department of Electrical Engineering, InstitutNational Polytechnique de Grenoble. Since 1989, hehas been a full Professor at University Joseph Fourier,Grenoble. He was a Visiting Professor in the SwissFederal Polytechnic Institute in Lausanne in 1989and in Campinas University (Brazil) in 2010. He has

been the Deputy Director of the Grenoble images, speech, signal, and controllaboratory (GIPSA, 300 people) and Director of the Department Images-Signal(DIS, 100 people) from 2007 to 2010. For 30 years, his research interests areblind source separation, independent component analysis, and learning in neu-ral networks, including theoretical aspects (separability, source separation innonlinear mixtures, sparsity) and applications in signal processing (biomedical,seismic, hyperspectral imaging, speech). He is an author or co-author of morethan 65 papers in international journals, four books, 22 invited plenary talks,and 150 communications in international conferences.

Dr. Jutten was an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS

AND SYSTEMS in 1994–1995, and co-organizer the 1st International Conferenceon Blind Signal Separation and Independent Component Analysis (Aussois,France, January 1999). He has been a scientific advisor for signal and imagesprocessing at the French Ministry of Research from 1996 to 1998 and for theFrench National Research Center (CNRS) from 2003 to 2006. He is currentlyDeputy Director of the Institute for Information Sciences and Technologies ofCNRS. He received the Medal Blondel in 1997 from SEE (French ElectricalEngineering Society) for his contributions in source separation and independentcomponent analysis, and became a Senior Member of the Institut Universitairede France in 2008.

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